Nonlinear Fiber Optics - 4 ed. Agrawal

162 Chapter 5. Optical Solitons
Figure 5.19: (a) Temporal and (b) spectral evolutions of a second-order soliton (N = 2) over five
dispersion lengths for s = 0.2.
different speeds. As a result, they separate from each other, and the separation increases
almost linearly with the distance [181]. The ratio of the peak heights in Figure 5.19 is
about 9 and is in agreement with the expected ratio (η 2 /η 1 ) 2 , where η 1 and η 2 are the
imaginary parts of the eigenvalues introduced in Section 5.2.1. The third- and higherorder
solitons follow a similar fission pattern. In particular, the third-order soliton
(N = 3) decays into three solitons whose peak heights are again in agreement with
inverse scattering theory.
5.5.4 Intrapulse Raman Scattering
Intrapulse Raman scattering plays the most important role among the higher-order
nonlinear effects. Its effects on solitons are governed by the last term in Eq. (5.5.8)
and were observed experimentally as early as 1985 [188]. The need to include this
term became apparent when a new phenomenon, called the soliton self-frequency shift,
was observed in 1986 [189] and explained using the delayed nature of the Raman response
[190]. Since then, this higher-order nonlinear effect has been studied extensively
[191]–[210].
Let us focus first on a fundamental soliton and consider the prediction of the moment
method. We isolate the effects of intrapulse Raman scattering by using β 3 = 0
and ω 0 → ∞ in Eqs. (5.5.3) through (5.5.6). The main effect of the Raman term is to
shift the soliton frequency Ω p that changes along the fiber length through Eq. (5.5.6).